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How to use law of sines when you have one solution

414 views · Published 26 April 2012 · 6:54 · Indexed 20 September 2026

Channel: Brian McLogan · 2012 · Education

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👉 Learn how to determine if a given SSA triangle has 1, 2 or no possible triangles. Given two adjacent side lengths and an angle opposite one of them (SSA or ASS), then there are 3 possible cases: there can be 1 solution, 2 solutions, and no solution. 

Using the law of sines, we can obtain the value of the angle opposite the second given side length. 
Case 1: If the product of the sine of the given angle and the given side adjacent to the given angle is greater than the given side opposite the given angle, then there is no possible solution satisfying the given values.
Case 2: If the obtained angle is greater than the given angle, then there are 2 possible solutions satisfying the given values.
Case 3: If the obtained angle is less than the given angle, then there is only 1 possible solution satisfying the given values.

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Organized Videos:
✅ Law of Sines
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoSv8cypcRnfkJdxWp02622
✅ Determine 1, 2 or No Triangle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpHLqyVTeoeFO9pHziapdOM
✅ Law of Sines | Learn About
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoKvxj3KTYEoJzz9WIyxTcC
✅ Law of Sines | ASA
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp0Wkn3bvlbA_NxQxtibqfi
✅ Law of Sines | AAS
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoMYbsUKx8-IkuZynqyflqj
✅ Law of Sines Ambiguous Case 2 Triangles
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMo8MMldMYzCUiQgdOeWiIJr
✅ Law of Sines Ambiguous Case 1 Triangle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoewwFmBZIw3A3UuXfYJtI9
✅ Law of Sines Ambiguous Case No Triangle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqAWofxWk71ulJcH12Du84i
✅ Ambiguous Case Law of Sines | Learn About
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMq98rh3vv1dv2mNEY8bvkYp
✅ Find the Area of an Oblique Triangle SAS
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMopITRA5z0FQAx912ODqKXI

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